use NMA to get the elastic properties of loop

(originally written by Yuye Tang) A key procedure of the molecular-dynamics decorated finite element method (MDeFEM) is to determine the effective properties of components of a macromolecule. Here I illustrate how could one use the NMA computed from MD to estimate the elastic properties of loops in mechanosensitive channels, which is related with my research.

From the NMA computed from MD, a series of eigenvectors and eigen values of atoms are calculated. The parallel finite element model based on the main chain of the loop can be also constructed and its eigenvalues can be computed by, e.g. ABAQUS. The elastic constant of each residue is assumed to be an unkown. Therefore, the constrained variable metric algorithm can be used to solve the unknowns as follows:

1. assume the initial constants

2. use the algorithm to solve [K]{qj}=lj[M]{qj} eigenvectors and eigenvalues

3. calculate the error(x) = sum [((lj)c/(lj)m-1)^2+ ((qj)c/(qj)m-1)^2]

4. iteration to minimize this error

Finally, the optimized parameters could be calculated. This can be implemented into the MDeFEM model and employed for simulation of the gating of mechanosensitive channels.